You are confused about what Form 8332 means. If you are the custodial parent (the one the child lived with for at least 183 nights) and you sign 8332, the non-custodial parent gets the child tax credit. The custodial parent still gets earned income credit, childcare credit, education credit (if the child is in college), and can file as Head of Household.
YES .... you must enter the child in the program and answer all the following questions to indicate you signed the 8332 to waive the child to the other parent. Then the child will be listed as "non dependent, EIC qualified".
There is a special rule in the case of divorced & separated (including never married) parents. When the non-custodial parent is claiming the child as a dependent/exemption/child tax credit; the custodial parent** is still allowed to claim the same child for Earned Income Credit, Head of Household filing status, and day care credit. This "splitting of the child" is not available to parents who lived together at any time during the last 6 months of the year; then only one of you can claim the child for any tax reasons. The tax benefits may not be split in any other manner.
Note in particular that the non-custodial parent can never claim the Earned Income Credit, Head of Household filing status or the day care credit, based on that child, even when the custodial parent has released the exemption to him.
So, it's good idea to let the other parent know that you will be claiming those items, as many first time divorced parents are not aware of this rule and may try to claim those items, which will cause the IRS to send out letters.
Scroll down to "Children of divorced or separated parents (or parents who live apart)"
** The IRS goes by physical custody, not legal custody, for who is the custodial parent. Furthermore, for tax purposes, there is no such thing as joint custody, regardless of what your legal agreement says. The requirement, to be custodial parent, is that the child live with you MORE than 50% of the time. One of you has to be the custodial parent and the other the non-custodial parent. The IRS goes by physical custody, not legal custody.